BR102014001496A2 - method for automatically characterizing an echo contained in an ultrasonic signal, and system for automatically characterizing an echo contained in an ultrasonic signal - Google Patents

Abstract

method for automatically characterizing an echo contained in an ultrasonic signal, and system for automatically characterizing an echo contained in an ultrasonic signal. An example method for automatically characterizing an echo contained in an ultrasonic signal generated with an ultrasonic transducer may include receiving data corresponding to the ultrasonic signal, calculating an energy ratio of the ultrasonic signal, and locating the echo using the energy ratio. The method may include framing a portion of the ultrasonic signal around the localized echo and calculating a fast fourier transform (fft) and a hilbert envelope of the framed portion. The method may include estimating m echo parameters from the hilbert fft and envelope of the framed portion, where each of the m parameter vectors includes a plurality of echo parameters, calculating m parameter echo models based on each of the m vector vectors. echo parameter and iteratively minimize a difference between the framed portion of the ultrasonic signal and a sum of the m parametric echo models.

Description

METHOD FOR AUTOMATICALLY CHARACTERIZING AN ECO IN A ULTRASONIC SIGNAL, AND SYSTEM FOR AUTOMATICALLY CHARACTERIZING AN ECO IN A ULTRASONIC SIGNAL

BACKGROUND [001] Non-destructive evaluation (NDB) is a widely used technology for evaluating quantitative properties of unknown surfaces such as thickness, shape and texture. In ultrasonic echo pulse methods, scattered echoes from the surface contain essential information regarding reflector properties. Thus, it is desirable to correctly extract this information (eg in terms of amplitude, arrival time and center frequency). The parameters for arrival time, amplitude and central frequency were widely used in ultrasonic applications. For example, a technique in which reflected scatter echoes are modeled as noise-corrupted overlapping Gaussian echoes is known in the art. Additionally, algorithms based on Expectation Maximization (.. for Expectation Maximization, EM) to estimate ultrasonic signals have been developed. EM-based algorithms use the Gauss-Newton or Levenbe rg-Marquat method to conduct an optimization search that is subject to landing hazard and minimal local. [002] To improve the success of these techniques, an appropriate initial assumption should be made for the echo parameters being sought. In many cases, the echo to be characterized is obscured by noise or a noisy baseline, which makes it difficult to form the initial assumption. In response, there have been several searches centered around noise removal from a signal to facilitate easier echo characterization. A significant portion of these initiatives use first-order statistical methods such as mediating (eg, stacking) to produce an estimate of a noisy baseline that contaminates a signal. First-order statistical methods work well to estimate a baseline when the variance of echo arrival times at a convergence is large enough (such that the echo arrivals at the convergence do not match). However, statistical methods have limitations when the. ECO arrivals do not follow a distribution known as first-order statistical methods, and even more elaborate statistical methods are insufficient to address the challenge.

SUMMARY [003] Systems, methods and devices for automatically characterizing one or more echoes contained in an ultrasonic signal are described herein. The ultrasonic signal may be generated with an ultrasonic transducer and reflected from a formation before being recorded by the ultrasonic transducer. Optionally, systems, methods and devices can operate in a single ultrasonic trace to automatically locate and couple an echo embedded in the noisy ultrasonic signal. According to the implementations described here, it is possible to build more accurate initial assumptions of one or more echo parameters, which improves the performance and robustness of an inversion algorithm (for example, the generalized space-shift expectation maximization algorithm (in space alternating generalized expectation (SAGE)) used to optimize echo parameters. Invert-chosen echo parameters can then be used to generate an image, for example an image of the formation from which the ultrasonic signal is reflected. An example method for automatically characterizing an echo contained in an ultrasonic signal generated with an ultrasonic transducer may include receiving data corresponding to the ultrasonic signal with the ultrasonic transducer, calculating an energy ratio of the ultrasonic signal, and locating the echo contained in the signal. using the energy ratio. The method may also include framing a portion of the ultrasonic signal around the localized echo and calculating a Fast Fourier Transform (FFT) and a Hilbert envelope of the framed portion of the ultrasonic signal. In addition, the method may include estimating M echo parameter vectors from the FFT and Hilbert envelope of the framed portion of the ultrasonic signal, calculating M parametric echo models based on each of the M echo parameter vectors, and iteratively minimizing a difference. between the framed portion of the ultrasonic signal and a sum of the M parametric echo models. Each of the M parametric vectors may include a plurality of echo parameters. Optionally, the energy ratio of the ultrasonic signal can be calculated and the echo contained in the ultrasonic signal can be located using the energy ratio by calculating an energy ratio function of the ultrasonic signal, where the function (£ «+ i 10 - .. 1 j / (i + a2 F, ota «), and identify a & i = x-LEi / maximum value of the ultrasonic signal energy ratio function.The maximum value may correspond to an approximate location of the contained echo In the energy ratio function above, Ex is energy at a given data point, ax and a2 are energy adjustment factors, L is a window length, Sf = * + i £ * is energy of Ef '= xi & noise energy and Etoml is total energy. [006] Alternatively or additionally, the energy ratio function of the ultrasonic signal can be calculated by inverting the data corresponding to the head-to-tail ultrasonic signal to head, calculate the energy ratio function of the inverted ultrasonic signal and identify a maximum value of the energy ratio function of the inverted ultrasonic signal. The maximum value of the ultrasonic signal energy ratio function may correspond to a left side of a first echo contained in the ultrasonic signal, and the maximum value of the inverted ultrasonic signal energy ratio function may correspond to a right side of the first echo contained in the ultrasonic signal. Alternatively or additionally. The energy ratio function of the ultrasonic signal can be calculated by ascertaining the data corresponding to the ultrasonic signal, calculating the energy ratio function of the trimmed ultrasonic signal and identifying a maximum value of the energy ratio function of the verified ultrasonic signal. The maximum value of the energy ratio function of the ultrasonic signal may correspond to a left side of a first echo contained in the ultrasonic signal, and the maximum value of the energy ratio function of the trimmed ultrasonic signal may correspond to a left side of a second. echo contained in the ultrasonic signal. Optionally, the window length (in English for length, L) may be approximately equal to sf, n- where s is a tuning coefficient, fc is a central frequency of the ultrasonic signal and fs is a frequency. sampling Alternatively or additionally, a portion of the ultrasonic signal around the localized echo may be optionally framed by applying a half-Hanning taper to data corresponding to one or more sides of the ultrasonic signal outside the framed portion of the ultrasonic signal. Optionally, a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models can be iteratively minimized by performing at least one of a Gauss-Newton (GN) optimization, a genetic algorithm. Genetic Algorithm, GA) and a meta-heuristic approach to evolutionary optimization. Alternatively or additionally, the M parametric echo models can be calculated by calculating M parametric echo models based on each of the M echo parameter vectors and the framed portion of the ultrasonic signal. In addition, a difference between the portion ultrasound signal and a sum of the M parametric echo models can be significantly minimized by determining the plurality of echo parameters for each of the M base echo tone parameter vectors in each of the M parametric echo models, updating the M echo parameter vectors, determine if the updated M echo parameter vectors converge with the M echo parameter vectors and if convergence is not obtained, calculate M parametric echo models based on each of the M echo parameter vectors. updated echo and the framed portion of the ultrasonic signal. The process for iteratively minimizing a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models can be repeated until convergence is achieved. In addition, the method may optionally further include filtering the data corresponding to the ultrasonic signal to remove at least one baseline component of the ultrasonic signal. Alternatively or additionally, the plurality of echo parameters may include at least one of a bandwidth factor (a), an arrival time (r), a center frequency (fc), a phase (φ) and an amplitude (β). Optionally, the method may further include generating an image using the plurality of echo parameters. An example system for automatically characterizing an echo contained in an ultrasonic signal may include an ultrasonic transducer configured to generate and receive an ultrasonic signal and a control unit including at least one processor and memory. The ultrasonic transducer can optionally be located in a hole. The control unit can be configured to receive data corresponding to the ultrasonic signal from the ultrasonic transducer, calculate an energy ratio of the ultrasonic signal, and locate the echo contained in the ultrasonic signal using the energy ratio. The control unit may be further configured to frame a portion of the ultrasonic signal around the localized echo and calculate an FFT and a Hilbert envelope of the framed portion of the ultrasonic signal. In addition, the control unit can be additionally configured to estimate M echo parameters from the FFT and Hilbert envelope of the framed portion of the ultrasonic signal, calculate M parametric echo models based on each of the M echo parameter vectors, and minimize iteratively a difference between the framed portion of the ultrasonic signal and a sum of the parametric echo models. Each of the M parameter vectors may include a plurality of echo parameters. It should be understood that the subject matter described above may also be implemented as a computer controlled apparatus, a computer system or an industrial product, as a computer readable storage medium. Other systems, methods, features and / or advantages will or may become apparent to a person skilled in the art upon examination of the following drawings and detailed description. All such additional systems, methods, features and / or advantages are intended to be included in this description. and are protected by the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS The components in the drawings are not necessarily to scale in relation to each other. Similar reference numerals designate corresponding parts in all various views. Figure 1 is a diagram illustrating a pulse-echo configuration of an ultrasonic transducer with a corresponding signal. Figures 2A-2C are graphs illustrating exemplary ultrasonic signals received on a transducer. Ultrasonic. Figures 3A-3B are tables illustrating the effect of each parameter (for example, bandwidth factor, arrival time, center frequency, phase, and amplitude) on a parameterized waveform. 4A-4E. are graphs illustrating a sample pulse-echo waveform parameterized using a model order of two (for example, M = 2). Figures 5A-5D are graphs illustrating an example pulse echo signal recorded in a hole and corresponding energy ratio calculations. Fig. 6 is a graph illustrating the echo located at the example pulse-echo signal shown in Fig. 5A. Figures 7A-7D are graphs illustrating the impact of using different window lengths for the energy ratio function. Figures 8-10 are graphs illustrating a plurality of coupling techniques in accordance with implementations discussed herein. [0026] Figure 11 is a graph illustrating the FFT of a framed portion of an example ultrasonic signal. Figure 12 is a flowchart illustrating example operations for automatically characterizing an echo contained in an ultrasonic signal. Figures 13A-13G illustrate the results of ultrasonic echo parameterization using three Gaussian echoes in a single trace of sample hole data. Fig. 14 is a graph illustrating an enlarged view of the parameterization of Figs 13A-13F within the framed portion of the ultrasonic signal. Fig. 15A is a graph illustrating an example trace containing an evident first echo arrival. Figure 15B is a graph illustrating an example trace without an evident first echo arrival. Figure 16A is a graph illustrating multiple ultrasonic signals measured in a hole. Figure 16B is a graph illustrating the echoes of the ultrasonic signals of figure 16A estimated by. parameterization process. Fig. 16C is a graph illustrating the portions of the measured ultrasonic signals of Fig. 16A after removing the extracted echoes from Fig. 16B. Figure 17A is a graph illustrating free field response of ultrasonic transducer. Figure 17B is a graph illustrating the observed pulse-echo responses from 6 mm to 45 mm. Figures 18A-18F are graphs illustrating the decomposition of an ultrasonic signal. Figures 19A-19C are graphs illustrating the comparison between a true echo produced by conducting a parameterization using a model order of 2 (M = 2) on traces recorded with a 10 mm, 20 mm ultrasonic transducer. and 30 mm of balance. [0039] Figure 20 is a limestone block used in imaging tests according to implementations discussed herein; and Figures 21A-21D are the imaging results for filtration and parameterization, respectively.

DETAILED DESCRIPTION Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. Methods and materials similar to or equivalent to those described herein may be used in the practice or testing of the present disclosure. As used in the specification, and the appended claims, the singular forms "one", "one", "o, a" include plural referents unless the context clearly dictates otherwise. The term "understanding" and variations thereof as used herein is used synonymously with the term "including" and variations thereof and are open, non-limiting terms. Although implementations are described to automatically characterize an echo in an ultrasonic signal generated and detected by an ultrasonic transducer disposed in a fluid-filled bore, it will be apparent to those skilled in the art that implementations are not limited thereto but are applicable to characterize. an echo in ultrasonic signals in other environments.

Ultrasonic Echo Processing Referring now to Figure 1, a diagram illustrating a pulse-echo configuration of an ultrasonic transducer 102 with a corresponding signal is. shown. The ultrasonic transducer 102 may optionally be an acoustic tool designed for implantation into a fluid filled bore. The acoustic tool may optionally include a plurality of ultrasonic transducers, for example, the acoustic tool may optionally be an acoustic antenna system. The hole may be drilled in a formation 110 containing a desirable fluid reservoir such as oil or gas. Ultrasonic transducer 102 may therefore be used to obtain information about formation 110 as discussed in detail below. Ultrasonic transducer 102 may include a bearing 104, a ceramic element 106 and a delay line 108. The ceramic element 106 may include one or more piezoelectric elements. When a voltage pulse is applied to a piezoelectric element, the piezoelectric element transmits a pressure wave (for example, an ultrasonic wave). When a reflected pressure wave is intercepted by a piezoelectric element, the piezoelectric element converts the intercepted pressure wave into a pulse of. voltage. Additionally, the delay line 108 may be optionally configured to control the ultrasonic pulse delay time transmitted or received by the ceramic element 106, to minimize ultrasonic pulse dispersion, to provide impedance matching between transmitter and receiver, etc. Ultrasonic transducers are well known in the art and therefore are not discussed in further detail below. Optionally, the ultrasonic transducer 102 may operate in a pulse-echo or reflex mode where the ultrasonic transducer 102 both emits an ultrasonic pulse and receives the reflected ultrasonic pulse. For example, the emitted ultrasonic pulse may travel through a fluid 120 (e.g., water or mud) and may reflect out of formation 110 before returning to the ultrasonic transducer 102. The reflected signal may be captured as a measured electrical voltage. Such a measurement is referred to as a pulse echo. Pulse echo 13 OA-B is shown in Figure 1. It should be understood that pulse echo may be the result of reflection outside the mud interface (for example, a mud interface 130A echo) and / or 110 (e.g., a training echo 130B). Additionally, the pulse-echo amplitude 130 AB is affected by the amount of gas present in the mud as shown in Figure 1. In addition, it should also be understood that the ultrasonic transducer 102 can measure trigger noise 140. [0044] Measurements Pulse echoes can be used for imaging purposes, for example, imagining formation 110. The basis for creating an image comes from two measured attributes of the acquired pulse echo waveform - travel time and amplitude. It should be understood that the displacement time is a period of time between excitation (or triggering) of the ultrasonic transducer 102 and reception of the reflected ultrasonic echo. Travel time can be directly correlated to hole size and shape. It should be understood that the amplitude of the reflected ultrasonic pulse (for example, the echo pulse waveform) can be used to characterize the acoustic impedance of fluid 120 as well as formation 110, including fractures, texture, druses, etc. optionally, to extract the above attributes, a Hilbert envelope of the pulse-echo waveform can be calculated. The maximum peak amplitude of the Hilbert envelope and the location at which the maximum peak occurs correspond respectively to the amplitude and displacement time of the main echo in the pulse-echo waveform. As discussed in detail below, the basic principle of extracting the above attributes is complicated in effective practice. • ultrasonic transducer 102 may be operatively connected to a control unit 150. It should be understood that the control unit 150 may optionally be located above, on and / or below the surface of the formation 110. Alternatively or additionally, the control unit 150 It can be integrated with the ultrasonic transducer 102 and arranged in the hole. The ultrasonic transducer 102 and the control unit 150 may be connected by a communication link. This disclosure considers the communication link to be any appropriate communication link. For example, a communication link may be implemented by any means that facilitates data exchange between the ultrasonic transducer 102 and the control unit 150 including, but not limited to, wired, wireless, and optical links. The control unit 150 may optionally be configured to control the ultrasonic transducer 102 as well as receive, process and store acoustic data (for example, acoustic data detected, collected, recorded, etc. by the ultrasonic transducer 102). more basic, control unit 150 typically includes at least one processing unit and system memory. Depending on the exact configuration and type of control unit 150, system memory may be volatile (such as random access memory (randotn Access memory, RAM)), nonvolatile (as read-only memory). para read-only memory, ROM), flash memory, etc.), or some combination of the two. The processing unit may be a standard programmable processor that performs arithmetic and logic operations required for control unit 150 operation. [0045] For example, the processing unit may be configured to execute computer-readable coded program code, tangible. Computer readable media refers to any medium that is capable of providing data that causes the control unit 150 (that is, a machine) to operate in a specific mode. Various computer readable media may be used to provide instructions to the processing unit for execution. Computer readable recording media, tangible for example, include, but are not limited to, an integrated circuit (eg, field-programmable port arrangement or application-specific IC), a hard disk, an optical disk, a magnetic disk, optical disk, a floppy disk, a magnetic tape, a holographic storage medium, a solid state device, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage, or other magnetic storage devices. In addition, the control unit 150 may have additional functionality / features. For example, control unit 150 may include additional storage such as removable storage and non-removable storage including, but not limited to, magnetic or optical tapes or discs. Control unit 150 may also contain network connection (s) that allow the device to communicate with other devices. Control unit 150 may also have input device (s) such as a keyboard, mouse, touch screen, etc. Output device (s) such as display, speakers, printer, etc. may also be included. Additional devices may be connected to the bus to facilitate data communication between control unit 150 components. All such devices are well known in the art and need not be discussed at length here. Referring now to Figures 2A-2C, graphs illustrating example ultrasonic signals received on an ultrasonic transducer are shown. The ultrasonic signal is made up of two components - a baseline and a measured pulse-echo waveform (for example, the reflector pulse-echo response or the pulse-echo response). Baseline includes the transducer excitation pulse and response as well as noise, for example, in Figures 2A-2C, the ultrasonic signals are composed of three distinct regions: the ultrasonic transducer excitation pulse that occurs from approximately 0 ps to 10 ps, followed by the ultrasonic transducer response (for example, showing a tapering tap down from 10 ps onwards), and finally, the reflector pulse-echo response by approximately 30 ps. Figure 2A is a graph illustrating the ultrasonic signal produced by a baffle positioned approximately 10 mm from the ultrasonic transducer. Figure 2B is a graph illustrating the hidden echo pulse at the baseline of Figure 2A. Figure 2C is a graph illustrating the ultrasonic signals produced by reflectors positioned approximately 10 mm, 20 mm and 30 mm, respectively from the ultrasonic transducer. The amplitude and arrival time of the reflector pulse-echo response (eg, the pulse-echo response) can be extracted by means of a Hilbert envelope. Hilbert envelope peak peak time and amplitude can be used as the two attributes of the pulse-echo response for imaging purposes. It must be understood that there is some degree of error that exists. reading the two attributes from the Hilbert envelope due to the touch that is inert to the ultrasonic transducer. The severity of this error depends on the time the reflex echo arrives in relation to the touch of the ultrasonic transducer, where earlier arrivals may be obscured further by the initial touch of the ultrasonic transducer. In light of the amplitude and arrival time attribute errors introduced by the touch of the ultrasonic transducer, it is optionally desirable to remove this touch baseline from the acquired ultrasonic signal. All traces at a specific convergence will be contaminated with such a transducer touch. To address the issues that arise from this touch baseline problem, a parameterization technique, which is discussed in detail below, can be used.

Parameterization Extracting the exact amplitude and arrival time attributes is a matter of detecting the first peak in the pulse-echo response and the corresponding time at which the first peak occurs. When the signal-to-noise ratio (SNR) is sufficient, the extraction of pulse-echo response attributes can be a trivial matter, for example by applying the envelope. Hilbert However, in cases when sufficient SNR does not exist (for example, in the presence of a strong touch), the arrival time and pulse-echo response amplitude I attributes may contain errors. As discussed above, to remove the baseline from an ultrasonic signal to facilitate extraction of the pulse-echo response from the ultrasonic signal, statistical techniques such as mediating (or stacking) were used to produce an estimate of the line. that is contaminating the pulse-echo response. Statistical techniques can work well to estimate the baseline when the arrival time range of the convergence echoes is large enough that the echoes do not overlap with each other. For any kind of statistical technique to be successful, there must be a portion of a trace somewhere in the convergence that contains no baseline, otherwise the true signal portion will be added to the baseline estimate. Essentially, the problem manifests itself when echo arrivals do not belong to a known distribution. For logging-while-drilling (LWD) profiling tools, the nominal equilibrium range is difficult to control and typically ranges from 0.4 inch to 1.00 inch. Because of this narrow equilibrium range, it can be difficult to effectively remove the baseline using statistical techniques. Parameterization is an alternative technique that can be used to remove the pulse-echo response from the ultrasonic signal. Through parameterization, information contained in multiple traces is not trusted, and instead, only a single trace of ultrasonic data can be optionally used. Additionally, it is possible to quantify and extract key features of the pulse-echo response (eg arrival time, amplitude, phase, center frequency, and bandwidth) in ultrasonic data directly in the time domain. This is true even under noise and overlap conditions. It is also possible to use custom molded pulse-echo response molded models that are being sought. By doing so, a specific ultrasonic trace can be decomposed into the pulse-echo response and the baseline-containing residual of a single trace. In this way, the obstacle of low equilibrium variances is deflected. In addition, the amount of data that must be recorded may be reduced. Parameterization can be viewed as a form of loss data compression. In a downhole environment, where memory size is a scarce commodity, reducing the volume of recorded data allows for the possibility of recording data for a longer period of time. For example, instead of recording a trace length 256 signal by parameterization, the pulse-echo response can be represented by 5 parameters.

Gaussian Echo Model Gaussian echo model can be chosen because it is well suited for characterizing ultrasonic signals. A single echo from a reflector can be represented by: (D [0052] incorporating the shape of an Gaussian envelope. The echo parameters are stored in a vector Θ, which is composed of five variables: a bandwidth factor (MHz2) r arrival time (ps) fc center frequency (MHz) φ phase (rad) β amplitude (V) [0053] the values of the parameter vector Θ correspond directly to the physical properties of (reflector) The arrival time τ refers to the distance from the reflector (eg the hole wall) a, the bandwidth factor, is the echo duration in the time domain fc is a product of the center frequency. The amplitude β and phase responsáveis are responsible for impedance and size and orientation (eg, inclination) for the reflector.Figure 3 is a table illustrating the effect of each parameter on the paramed waveform.

Observation Model of an Ultrasonic Echo [0054]. A Gaussian wavelet lends itself well to modeling and approximating ultrasonic signals. The observed modulus of a single ultrasonic echo including noise and other artifacts can be represented as: x (t) = s (6?; T) + v (t) - cos (2nfc (t - r) + o) + v ( £) · (2) where s {0; t) is the ultrasonic echo and is responsible for noise and error. (for example, the ultrasonic signal component not covered in the parameterization). The Gaussian echo model can be extended to approximate echoes of greater complexity through the overlapping principle. For example, the approximation of an echo pulse, y (t), can become a sum of M overlapping Gaussian echoes as: j (t) * = Σ "= 1 <* μ; 0 + (3) [0057] Parameter vector 0m defines the shape and location of each individual echo.'As with a single echo parameterization, v (t) is the residual that includes noise and approximation error due to complexities that cannot be incorporated into the model. [0058] Referring now to Figures 4A-4E, graphs illustrating an example pulse-echo waveform parameterized using a model order of two (for example, M = 2) are shown. Figures 4A and 4B respectively illustrate the two individual Gaussian echoes 402 and 404 (for example, the first arriving at 26,979 ps and the second at 32,0276 ps.) The original pulse-echo waveform 406 (e.g. , the ultrasonic signal) is illustrated in Figure 4. As discussed here, the ultrasonic signal is the data recorded by the Ultrasonic transducer The sum of the two individual Gaussian echoes 4 02 and 4 04 produces the overall estimate of the incoming echo. This estimate (or reconstruction) 408 is shown relative to the original pulse-echo waveform 406 in Figure 4D. In Figure 4C, the difference between the reconstruction 408 and the original pulse-echo waveform 406 forming the remainder 410 (e.g., v (t)) is shown. The remainder 410 includes the second and third echoes, which have less value in parameterizing the pulse-echo response because those echoes contain limited information for imaging. By parameterization,. The ultrasonic signal (for example, the original pulse-echo waveform 406 of Figure 4E), which is approximately 5000 samples long, can be reduced to a parametric description using two Gaussian echo ripples, each including 5 elements (ie. , 10 parameters in total). The region where the first echo exists, which is the focal point of the parameterization, was approximated with less than 2% error. Additionally, it is also worth noting the substantial reduction in data volume that was realized where the 10 echo parameter representation provides a 50-fold reduction in data volume compared to the original recording of the first raw echo waveform ( 500 samples). Table 1 below shows the estimated parameters for the two individual Gaussian echoes 402 and 404 of Figures 4A and 4B. Having presented the parametric parametric constructor (for example, the Gaussian echo model) and the form of its implementation in the general observation model of a pulse-echo waveform, the determination of the optimal model parameters is. best describing the ultrasonic signal waveform are discussed in detail below. To produce an estimate of the ultrasonic signal, a comparison can be made between the echoes described in the parameterization and the ultrasonic echo of interest in the waveform. Changes in the parametric estimation in equation (1) above (that is, s (Θ; t)) are governed by observations on the input signal x (for example, the signal recorded in the ultrasonic transducer). The transformation from parameter space to signal space is nonlinear although it is described by an empirical Gaussian echo model. Therefore, the inversion process is also nonlinear. Additionally, the adaptation of an empirical model to real data is obscured by noise and touch, which complicates parameter estimation. To address this nonlinear parameter estimation problem, a Maximum Likelihood Estimation (MLE) framework is provided below. MLE is found by minimizing an objective function comprised of the observed data x (eg, the ultrasonic signal) and current parametric signal models (Θ) such as: (4) [0062] The objective is to minimize the difference between the data. observed and the parametric estimate. When computing the objective function, it is evident that it is nonlinear in the vector Θ. Because of this, the optimization problem is established as a non-limited nonlinear least squares (LS) problem because there is no limited region in the parameter vector. Algorithms for solving non-limited LS problems operate in an iterative mode. To begin with, an initial assumption is made for the parameter vector, and with each iteration, the parameter vector undergoes refinements to minimize objective function. When the objective function reaches a minimum, the optimal parameters were found (eg a global minimum). It should be understood that the local minimum may exist and depending on the initial assumption, the algorithm may be trapped in one of these minimum locations, resulting in a suboptimal solution. Therefore, it is desirable to determine the initial parameters to ensure optimal convergence.

Gauss-Newton Optimization Gauss-Newton (GN) optimization can optionally be used to solve the above-mentioned non-limited LS problem. With each iteration of the GN process, the parameter vector Θ is updated, resulting in an improvement in the objective function. This disclosure considers the use of other techniques to solve the LS problem not limited, including but not limited to a genetic algorithm (GA), evolutionary optimization metaheuristic approach, or particle cluster optimization. to Particle Swarm Optimization, PSO). The GN update formula can be written as: (5) where 0k is the current parameter estimate and / # (©) is the model gradient with respect to the parameter vectors [cr τ fç φ β ]. (x - 5 (0 ^)) is the difference between the observed signal and the current parametric reconstruction. The vector Η (θ) is comprised of partial derivatives of each parameter. These partial derivatives are expensive to compute, which is an important consideration because to update them, partial derivatives are recomputed with each iteration. With this in mind, to accelerate computation, Gaussian echo analytic gradients can be used. The gradient matrix is written as: (6) (7) (8) (9} (10) (11) To further reduce computational complexity, the inverse of the gradient matrix (^ Ητ can be computed: [ The inversion algorithm can include the following steps: Step 1: Begin with an initial assumption for the parameter vector [Step 2: Compute the ü (0k) and s (0k) gradients ), [0072] Step 3: Iterate the parameter vector: [0073] Step 4: Check the convergence criterion against a predetermined tolerance: [0074] \\ 9k + 1 - Gk \ l <tol, where tol is the difference between two consecutive parameter iterations It should be understood that as the parameter vector is iterated, improvements in each of the parameters included in the parameter vector become marginal.Tolerance is a measure of the marginal change between the new parameter vector estimate. parameter (eg θ ** 1) and the previous parameter vector estimate (eg 9k ).

This revelation considers that the difference can; be calculated as an absolute change or as a percentage change between the new and previous parameter estimates. For example, the tolerance can be optionally set to tol = 0.01, which ensures that the algorithm converges and that subsequent refinements are negligible. This revelation considers defining tolerance in other values. If convergence has been achieved, otherwise end go to step 5. Step 5: set kr ^ k + 1 (and continue iteration).

Parameter Initialization [0076] To parameterize an ultrasonic signal, it is desirable to make an accurate initial assumption of the initial parameter vector. As discussed above, an accurate initial assumption can improve the chance of finding the optimal solution as well as reduce the number of computations required to find it. To make an accurate initial assumption, a multistage process of removing bias or removing the baseline from the ultrasonic signal, locating the echo on the ultrasonic signal, and framing the ultrasonic signal before parameterization is discussed in detail below. As discussed above, the ultrasonic signal may be a unique trait.

Baseline Removal [0077] Optionally, a baseline removal operation can be applied to the ultrasonic signal to make the first echo pulse easier to identify. There are two components that contribute to the baseline that can be removed. The first originates from the excitation pulse of the ultrasonic transducer. The second originates from the ultrasonic transducer which experiences a call cut of the excited piezoelectric element, which takes some time to slow down. In addition to the touch of the piezoelectric element, there may also be some touch from the front face window that protects the element. When the echo arrives too early (for example, when the reflector is set to a low equilibrium), then the initial echo may arrive while the ultrasonic transducer is still ringing.

This touch can be affected by heat and temperature and the relationship is nonlinear. To remove the baseline, three techniques were used, each technique operating in multiple strokes to form the estimate for the baseline. Stacking is a commonly used technique for improving SNR in seismic data. The principle behind stacking is to form a baseline estimate by computing an average of the observed traces. Components in the unchanging strokes such as the trigger response and the touch of the ultrasonic transducer, for example, may form the baseline. Additionally, the components in the unchanging features occur in every feature. Thus when the convergence traits are mediated, the changing components can be mediated with the non-mutant components to form the baseline estimate. [0079] Another technique that can be used to estimate the baseline is singular value decomposition (SVD). SVD is a decomposition and .. classification of the trace components in a convergence based on the level of variance that the traits present among themselves. SVD can be used to explore the major baseline trend that contaminates the traces in an ultrasonic convergence. Because all traits in convergence share a common baseline, the baseline component has the highest rating. The other remaining contributing components such as echoes and noise, for example, are typically poorly correlated and should manifest in SVD decomposition at a much lower rating compared to the baseline. Using the upper SVD value as the baseline works similarly to stacking it with the same advantage, that is, if the echoes in the convergence traces do not have enough variance, the echoes may be major contributors to the baseline. in decomposition. In addition, SVD is significantly computationally more expensive than simply averaging all traits in convergence. [0081] Alternatively or additionally, subtraction is another technique that can be used to estimate the baseline. For example, if the ultrasonic echoes in two strokes are sufficiently separate (for example, the echo lengths do not coincide at the same time), then the baseline can be calculated by subtraction. For example, two ultrasonic signals S2 and S2l which are both comprised of two sufficiently spaced echoes and a common baseline are given below: S ± = Εχ + B (13) S2 = E2 +. B (14) Sx - S2 = Ei - Ez (15) Subtracting the two ultrasonic signals from each other can provide a trace that is exactly two echoes Ex and E2, free from any baseline. It should be understood that the requirement that echoes do not interfere with each other due to overlap is important. If echoes overlap, it is possible to have an adverse effect on the overall amplitude of one or both echoes due to constructive or destructive interference. After performing the subtraction, the echoes can be extracted by applying two couplings to the ultrasonic signals and subtracting the echoes from their respective trace. Coupling of ultrasonic signals is discussed in detail below. The result provides a baseline approximation that can be used to remove noise from ultrasonic signals at convergence.

Echo Locating Using an Energy Ratio Technique After optionally preprocessing the ultrasonic signal by trending and removing the baseline components, the region in the trace that contains the first echo can be identified (or localized). The motivation behind the location of the region in which the first echo is hidden is twofold.

First, locating the first echo facilitates a reduction in overall data volume. In addition, the location of the first echo improves accuracy because parameterization efforts can be focused on a much tighter region (for example, a narrower search space). One technique for locating the first echo is by calculating the energy ratio of the trace. Using the energy ratio function, the energy at a given point Ex is calculated using the following formula: (16) where, ai = energy adjustment factor 1 energy signal a2 = energy adjustment factor 2 II = energy of noise L - jean length 1 to '£' total = total energy [0085] It should be understood that equation (16) is provided only as an example of an energy ratio function and that a person of ordinary skill in the art can calculate the energy ratio function of the trace in a different mode. [0086] A given point x may be framed from either the left or right side of the trace using a window in length, L. The energy content in the left and right window is assumed to be noise and signal, respectively. The ratio is constructed by comparing signal energy with noise energy. Additionally, the cumulative sum of the energy residing in the total signal, Etotaj, can be computed. Adjustment factors ax and a2 can be used to minimize the impacts of late arrivals in estimating the first movement estimate. The first break in the signal is indicated by the location of the maximum value of the energy ratio function. An example ultrasonic signal measured in a hole is used to illustrate this location technique. Example ultrasonic signal 502 is shown in figure 5A. The ultrasonic signal 502 includes 512 samples covering from 0 ys to 170.66 ys (for example, a 3 MHz sampling rate). The left-to-right ultrasonic signal 502 '(ie, the moved ultrasonic signal) is shown in figure 5B. In other words, the ultrasonic signal is inverted from head to tail to tail to head. For example, in Figure 5A, samples 0-511 are arranged from left to right. In Figure 5B, samples 0-511 are arranged from right to left. The energy ratio of the ultrasonic signal 502 and the ultrasonic moved signal 502. ' can be calculated using equation (16) above with a window size of 40 (L = 40) and energy adjustment factors ax and a2 defined in unit (i.e. 1). The energy ratio of the ultrasonic signal 502 is shown in FIG. 5C, and the energy ratio of the moved ultrasonic signal 502 'is shown in FIG. 5D. Maximum values of the energy ratio functions indicate the breaks in the ultrasonic signal and the moved ultrasonic signal. In other words, the energy ratio functions can be used to identify the left and right bursts of an echo in the ultrasonic signal. For example, the peak energy ratio of the ultrasonic signal in Figure 5A occurs at t = 66 ys. This locates the left echo arrival time (or the left echo rupture). The peak energy ratio of the ultrasonic signal moved in figure 5B occurs at t = 79.33 ys. This can be used to locate when the echo ends. For example, when the energy ratio of the moved ultrasonic signal is moved back from left to right (or inverted from tail to head to tail), the time resulting from the right echo break is t - 17 0.66 - 79.33 = 91.33 ys. Thus, the incoming echo was located by the position of the left and right ruptures (for example, 66 ys and 91.33 ys). Figure 6 shows the localized echo 602 of the ultrasonic signal 502 in figure 5A. [008 9] The window length, L, of the energy ratio function can determine the effectiveness of the energy ratio. Shorter window lengths produce higher resolution but higher noise sensitivity energy ratio functions. On the other hand, longer window lengths are more robust against noise at the expense of offering lower resolution power. It is therefore desirable to carefully select the window length such that it is noise insensitive while still being able to correctly determine the first break in the ultrasonic signal. Optionally, to automatically select the length of the energy ratio window, equation (17) below can be used. (17) Where fs and fc are the melt rate uj-ay cm and the center frequency of the ultrasonic signal, respectively. The multiplier, s, typically defined in units, is also included to tune the window length. based on time between multiple echo arrivals (governed by the properties of the environment in which the pulse echo response is recorded). According to equation (17), the window length may be automatically and dynamically adjusted in response to different sampling frequencies as well as acquisition time intervals. Referring now to Figures 7A-7D, graphs illustrating the impact of using different window lengths for the energy ratio function are shown. For example, Figure 7A shows an example 702 pulse echo recorded when a 250 kHz ultrasonic transducer is triggered on an aluminum reflector and a pulse echo signal is acquired at 25 MHz. The recorded waveform has three regions. exclusive, for example, first, second and third echoes 702A, 702B and 702C, respectively. As discussed above, the objective of echo location is to correctly identify the first break in the pulse-echo signal. Figures 7B-7D show the results of applying the energy ratio function to pulse echo signal 702 in Figure 7A using window lengths of L = 7, 75, 750, respectively. As shown in Figure 7B, when the window length is too small (e.g. L = 7), it is difficult to identify the first echo break because there is no easily distinguishable peak in the energy ratio function. Similarly, as shown in Fig. 7D, it is also difficult to identify the first echo rupture when the window length is too large (for example, L = 750). Specifically, the second echo break is detected by using a window length of 750 instead of the first echo break because the window length is greater than the location of the first echo (e.g. -500 samples). As shown in Figure 7C, when the window length is 75, the first echo break is correctly detected.

Echo Coupling After finding the first echo break in the ultrasonic signal, there are several techniques that can be used to couple the recorded echo. Referring now to Figures 8-10, graphs illustrating example coupling techniques are shown. In Figure 8, the energy ratio function is calculated from the left side of an ultrasonic signal. Then the ultrasonic signal is moved from left to right. In other words, the ultrasonic signal is inverted from head to tail to tail to head as discussed above with respect to figures 5A-5B. Subsequently, the energy ratio function is calculated from the right side of the ultrasonic signal. As discussed above, the energy ratio function from the left side can be used to find the first echo break, for example, the left break on the ultrasonic signal. Additionally, the right energy ratio function can be used to find the right break in the ultrasonic signal. The right break position is then moved from left to right so that it is properly positioned with respect to the left break. It should be understood that the left and right ruptures may be used to couple the first echo to the ultrasonic signal. The coupled portion 802 of each stroke (for example, the ultrasonic signal) is shaded in Figure 8. This technique can be quite robust and can dynamically couple the first echo. It should be understood, however, that if a second echo with sufficient amplitude exists, the second ecc can be detected as the right rupture. In this case, no data loss occurs, but the coupling is placed around the first break of the first echo and the tail end break of the second echo. [0095] In Figure 9, the energy ratio function is calculated from the left side of an ultrasonic signal. As discussed. Above, the energy ratio function from the left side can be used to find the first echo break, for example, the left break on the ultrasonic signal. Next, the ultrasonic signal is trimmed at the site of the first echo rupture. Subsequently, the energy ratio function is calculated from the left side of the trimmed ultrasonic signal. The energy ratio function from the left side of the trimmed signal can be used to find the next break in the ultrasonic signal, which corresponds to the second echo. It should be understood that the first and subsequent ruptures may be used to couple the first echo to the ultrasonic signal. The coupled portion 902 of each trace (for example, the ultrasonic signal) is shaded in Figure 9. This technique may be more robust than coupling on the left side of the ultrasonic signal and then coupling on the right side of the moved ultrasonic signal because There is typically some white space between the first and second echoes, which causes a large spike in the energy ratio function making it relatively easy to identify the second echo. It should be understood that when this technique is used there may be more redundant data (for example, the white space between the first and second echoes) included in the coupling. In figure 10, the energy ratio function is calculated from the left side of an ultrasonic signal. As discussed above, the energy ratio function from the left side can be used to find the first echo break, for example, the left break on the ultrasonic signal. Next, a hard coupling is defined from the left break position. The length of the hard coupling can be determined based on the expected duration of the first echo, originating from the medium in which the pulse echo travels. It should be understood that the first rupture and hard ruptures may be used to couple the first echo to the ultrasonic signal. The coupled portion 1002 of each trace (for example, the ultrasonic signal) is shaded in Figure 10. This technique may be computationally the lightest of techniques because only an energy ratio calculation is required. In addition, the calculation of the first echo break from the left side of the ultrasonic signal is more robust compared to the calculation of the energy function from the right side of the moved ultrasonic signal or again from the left side after ascertaining the ultrasonic signal. To demonstrate each of the three coupling techniques discussed above with respect to figures 8-10, an ultrasonic transducer operating in water was used to collect reflected data from a single reflector (eg, aluminum) at incrementally varying distances from the reflector. For example, the equilibrium range of the ultrasonic transducer from the reflector has been adjusted in 1 mm increments from 0 mm to 41 mm, (dashes # 1 to # 42, respectively, where trace # 1 corresponds to 0 mm equilibrium) which mpve the echo that arrives further away from the trigger response. The results of the demonstration are shown in figures 8-10, and some general observations are made below. As shown in figures 8-10, coupling from the left side of the ultrasonic signal is quite robust. For example, the first break in the signal is perfectly coupled down to 4 mm as shown in each of figures 8-10. Additionally, right-side coupling of the ultrasonic signal, for example, after moving the ultrasonic signal from left to right, is not as robust as coupling on the left-hand side of the ultrasonic signal. As discussed above, detecting the right burst of the first echo in the ultrasonic signal can be challenging when there are subsequent echoes (e.g., second, third, etc.) arriving at the same acquisition window. For example, if the peak pertinent to the second echo is stronger than the peak pertinent to the first echo, then when the energy ratio is applied, coupling will be applied to the tail end of the second echo rather than the tail end of the first echo. Echo When this occurs, the first and second echoes are both coupled as shown in dash numbers 21 through 37 as shown in figure 8. In addition, as shown in figure 9, the left break calculation and then the left break calculation following works well up to approximately 10 mm. As discussed above, this generates dash lengths that are somewhat long because the coupling spans the first echo and all white space to the second echo. By applying an echo coupling, it is also possible to exploit redundancy between echoes because they are all very similar when aligned to a common time reference. This benefit may well lend itself to applying compression to further reduce data volume in a convergence.

Model Order Selection [0098] The inversion result is a result of a sum of simultaneously optimized Gaussian echoes. The model order can determine the effectiveness of the overall approximation. of ultrasonic echo in hand. For example, using a high model order allows more complex waveforms to be approached but takes longer to converge on a solution. On the other hand, using a low model order is much less computationally intensive, but may require more iterations to converge on a solution. Therefore, it is desirable to correctly choose the model order required to approximate the echo. To maximize the effectiveness of parameterization regardless of the model order that is chosen, parameterization can be applied to a well-located region, for example by coupling the echo portion of the ultrasonic signal. Then the smaller localized region (or coupled portion) can be subjected to analysis by applying the Hilbert transform. The Hilbert transform can be applied to the removed and controlled signal to reduce computational cost, and the Hilbert envelope can then be examined. What the Gaussian echo is like. For an empirical model selected to better approximate the ultrasonic echo, a single model order may be appropriate for echo and may correspond to a single peak in the ultrasonic signal. By examining the Hilbert envelope of the Gaussian echo, the number of critical peaks can be determined. The number of peaks can be determined by means of a derivative based peak discovery function. A peak is indicated at the point in the Hilbert envelope derivative where the gradient changes from positive to negative. It should be understood that these points indicate the peaks in the function. To further refine the number of determined peaks, limitation may be applied in terms of amplitude as well as relative peaks between them. [00102] Next, the model order can be optionally selected as shown below: Bite = number of critical peaks detected in window + 1 [00103] The selected model order can be increased by 1 to be responsible for noise and aberrations. that may exist in the ultrasonic signal. Extra model ordering can be added to minimize noise since it is assumed that echoes can be obscured by noise and GN optimization is subject to minimization. If the extra model order is not added, the echo approximation within the window attempts to account for noise as well as the true echo in the window. By including the extra model order, the true echo can be adjusted in the models determined by the number of critical peaks in the window with the remaining model order absorbing non-empirical model deviations.

Initial Setting and Selection of Parameters After locating the echo contained in the ultrasonic signal, a portion of the ultrasonic signal around the localized echo can be framed. As discussed above with reference to Figure 6, the incoming echo was located between the left and right burst positions (for example, 66 ps and 91. ps). Optionally, a half-Hanning filter may be applied to taper portions of the ultrasonic signal outside the localized region (eg, <66 ps and> 91.33 ps). Alternatively or additionally, a window may be defined around the localized echo which is 50% as large as the localized echo length. For example, the window might be defined as: [66 - —-3 ^ ββ * *, 91.33 + HIHZI] = [52.67 ps, 106 ps]. Next, a half-Hanning taper can be applied at 5% to the regions outside the window to bring the ultrasonic signal ends to zero. Later, as discussed in detail below, the initial echo parameters can be selected. It should be understood that the application of a half-Hanning filter is provided as an example framing technique only and that other framing techniques may be used. Echo parameters can then be estimated from the framed portion of the ultrasonic signal. As discussed in detail below, estimates for amplitude and arrival time can be obtained by calculating a Hilbert envelope of the framed portion of the ultrasonic signal and estimates for center frequency and bandwidth can be obtained by calculating a Fourier transform (for example, using a FFT) of the framed portion of the ultrasonic signal. This disclosure assumes that other transforms known in the art may be applied to the framed portion of the ultrasonic signal to facilitate obtaining echo parameters. For example, a framed Fourier Transform and then a Hilbert transform can be applied to the framed portion of the ultrasonic signal.

Amplitude and Arrival Time [00106] Estimates for the initial amplitude and arrival time parameters, β and τ, can be defined from the framed signal envelope (Sw ± n), which is calculated by taking its absolute value. Hilbert transform (Η |. The location and amplitude of the maximum envelope value (ie maximum peak) corresponds directly to the echo amplitude, βχ and displacement time, τι. Initializations for subsequent models used in inversion (eg M = > 2} are defined by evenly distributing their positions between the maximum peak position and the end of the inversion window. [00107] When working with the first model order (eg M = 1), the echo amplitude and the offset time can be found as follows: (τι> βι) = ar gmax | H (J, iVi n) | (18) [00108] Additionally, when working with higher model orders (eg M> 2 ), a time step, Step / can be used, time is defined in equation (19) below. The time step is used to equally distribute the remaining model positions as defined by equation (20) below between the maximum peak location and the end of the inversion window, Linv. The Hilbert envelope value is used to define the initial amplitudes at these distributed points, which are defined by equation (21) below, For k = 2: M, (19) ¢ 20) ¢ 21) Center Frequency and Bandwidth [00109 ] The estimate for. The center frequency parameter, fc, can be set from the framed signal's FFT. For example, an FFT of the framed portion of the ultrasonic signal may be calculated. The FFT of the framed portion of the ultrasonic signal of Figure 7A is shown in Figure 11. The maximum value of FFT 1102 can be selected as the center frequency of the ultrasonic echo that must be parameterized. As shown in Figure 11, the maximum or peak value of FFT 1102 occurs at approximately 255 kHz. It should be understood that this also corresponds approximately to the frequency of the ultrasonic transducer discussed above with respect to Figure 7A. Additionally, when parameterization with a model order of 2 or higher is used, the same center frequency can be used to seed subsequent model orders. Until the maximum model order (Mmax) in inversion. Since FFT does not provide time location relative to where frequencies exist, all models in the inversion are initialized to the same center frequency. It should be understood that using the same center frequency for the initial center frequency parameter for higher model orders. This is sufficient because the other frequencies that make up the echo (eg ringing) are also close to the maximum frequency of the ultrasonic transducer. Equation (22) below can be used to select the initial center frequency parameter. For k = T: M, fck = argmax (FFT (Swin}) (22) [00110] The estimate for the width factor parameter The initial bandwidth, ak, can also be set from the framed signal FFT Similar to the center frequency, bandwidth can be selected using the maximum or peak FFT value 1102. To determine the approximate bandwidth of the ultrasonic echo, the left and right derivatives of the maximum FFT value can be computed until a signal change is observed A minimum is indicated when the derivative becomes positive Then on the left and right sides of the maximum FFT peak Minimum points are subjected to a linear fit extending downward towards the x-axis.The squared distance between the left and right minimum points on the x-axis can be used as the parameter estimate of 1a. It should be understood that the same bandwidth factor can be used for the estimation for all model orders. Equation (23) below can be used to select the initial bandwidth parameter. For k = 1: M, ak = (/ ίχ (23) Phase [00111] The initial estimate for the phase parameter, φ, can be set to zero for all model orders. The reasoning for this estimate is discussed - First, if the ultrasonic echo is composed of a single clean pulse, it could be possible to precisely calculate the instantaneous phase. However, the ultrasonic echo is typically composed of multiple overlapping components. The other initial model parameters discussed above are defined by initial estimation, which carries the same certain error without notions of how much overlap exists between them, so it is difficult to estimate a phase that is close to optimal Secondly, as the phase is cyclic and parameterization convergence is insensitive to its value, it is appropriate to set the initial phase to zero.

Inversion After the main echo contained in the ultrasonic signal has been located and framed, it is possible to invert to a plurality of echo parameters. As discussed above, the Gauss-Newton process can be integrated into an expectation maximization algorithm (EM). The EM algorithm has a structure where at each step the expected signals are computed using the current parameter vector estimate and the observed data (eg the ultrasonic signal). Next, the corresponding parameter sets are computed using those expected signals. Alternatively, you can update the parameter vector after the maximization step (for example, step M). By doing so, the current parameter estimation is integrated in step-E to accelerate convergence. This alternative method is known as the space-alternating generalized EM (SAGE) algorithm. Compared to traditional EM algorithms, the SAGE algorithm has a faster convergence property. Referring now to Figure 12, a flowchart illustrating example operations 1200 for automatically characterizing an echo contained in an ultrasonic signal is shown. As discussed above, an ultrasonic signal can be generated with an ultrasonic transducer. After reflecting from a reflector, data corresponding to the ultrasonic signal can be received with the ultrasonic transducer. Optionally, the ultrasonic transducer may be located in a fluid-filled bore, and the ultrasonic signal may be reflected from a formation. Optionally, data corresponding to the ultrasonic signal may be preprocessed, e.g. filtered, to remove or reduce bias and / or extraneous noise. The data may be preprocessed according to any of the techniques described herein. It should be recognized that the logical operations described herein in relation to the various figures may be implemented (1) as a sequence of computer implemented acts or program modules (ie software) that runs on a computing device, ( 2) as interconnected machine logic circuits or circuit modules (i.e. hardware) no. computing device and / or (3) a combination of computing device software and hardware. Thus, the logical operations discussed here are not limited to any specific combination of hardware and software. Implementation is a matter of choice dependent on performance and other computing device requirements. Accordingly, the logical operations described herein are variably referred to as operations, structural devices, acts or modules. These operations, structural devices, acts, and modules may be implemented in software, firmware, special purpose digital logic, and any combination thereof. It should also be recognized that a larger number. or minor operations can be performed than shown in the figures and described herein. These operations can also be performed in a different order than those described here. Optionally, at 1202, an ultrasonic signal may be preprocessed, e.g. filtered to remove or reduce bias and / or extraneous noise, as discussed above. At 1204, an energy ratio of the ultrasonic signal can be calculated and the echo contained in. Ultrasonic signal can be located using the energy ratio. The energy ratio can be calculated and the echo can be located according to any of the techniques discussed here. At 1206, a portion of the ultrasonic signal may be framed around the localized echo. • The ultrasonic signal can be framed according to any of the techniques discussed here. At 1208, an FFT and a Hilbert envelope of the framed portion of the ultrasonic signal can be calculated. Then, at.1210, the initial inversion parameters (eg, the initial parameter vectors, □ = ^ 2 ° i; ®i ??]) can be estimated from the FFT and Hilbert envelope of the framed portion of the ultrasonic signal. . It should be understood that the iteration number and echo number can initially be set to 0 (for example, k = 0 to = 0). In 1212, the parametric echo model (for example, the expected ultrasonic signal) to the ° echo. can be computed based on the current parameter vector CO and observed data y (eg | the ultrasonic signal), for example according to =) + - iy - EfLi 5 (¾}. Step 1212 can be referred to In 1214, using the parametric echo model computed above, a new parameter vector C®m + 1) can be computed, for example, as the maximum probability estimate (MLE) for (0 ^) . For example, the new parameter vector can be determined according to θ ^ 1 = argp rainllx ^, - s {0m) || 2. Step 1214 can be referred to as the Maximization Step. In other words, the Maximization Step corresponds to the MLE of a single echo with the parametric echo model for m ° echo, for example, x ^. Next, in the next Expectation Step, the parametric echo model for the signal. following or the m ° + l echo, for example, χϊ ^ + · ι can be computed using the newly updated parameter vector (θ ^ 1). At 1216, one m + 1, and the process returns to step 1212. If YES (for example, m> M), the process continues to step 1218, where a determination is made as to whether convergence is obtained. , for example, || 0fe + 1 - ek \\ <appreeterriúnedtoierance. In other words, a determination is made as to whether a change in the parameter vector between the current and previous iteration is less than a predetermined tolerance. If YES, the process ends and the plurality of echo parameters has been computed. If NO, the process continues to step 1212, for example, m is set to 1 and Jc is set to k + 1. Therefore, it is possible to iterate until the convergence criterion is obtained.

Examples: Real Data Parameterization Process Real Data (Single Trace) [00116] To demonstrate the result of the parameterization algorithm on a field-acquired real-world borehole data set, well test data were used. The data set is comprised of 1148 traces consisting of 512 samples each at a 3 MHz sampling rate. A sample from this data set was chosen to be parameterized using three Gaussian echoes (M = 3). Figures 13A-13G illustrate the results of ultrasonic echo parameterization using three Gaussian echoes in the sample bore data. Figure 13A is a table illustrating the optimal parameters for each of the Gaussian echoes obtained by the inversion process. Figure 13B is a graph illustrating the ultrasonic signal measured by the ultrasonic transducer disposed in the bore. Figure 13C is a graph illustrating the ultrasonic signal reconstructed using Gaussian echoes. Figure 13D is a graph illustrating the difference between the measured and reconstructed ultrasonic signals of figures 13B and 13C, respectively. Figures 13E-13G are graphs illustrating each of the Gaussian echoes. Additionally, Figure 14 is a graph illustrating an enlarged view of the parameterization shown in Figure 13C, for example, a framed portion of the ultrasonic signal.

Actual (Multiple Strokes) Data To apply the parameterization process to a large-scale data set, the rest of the strokes in the acquired hole data set were parameterized to specifically test the robustness of the framing functions and location. In the 1148 stroke data set, 95% of the strokes contain a clear first echo arrival. Figure 15A is a graph illustrating an example trace containing a first evident echo arrival. In the remaining 5% of. Traces, there is an obvious clock, however, no echoes arrive. Fig. 153 is a graph illustrating an example trace that does not contain an obvious first echo arrival. It was 95% of cases where a first echo is evident, the successfully localized parameterization algorithm framed and inverted for the first echo (eg 2% parameter accuracy with approximately 3Q iterations / 1 ms processing time using M = 3). In cases where no echo. It was evident that the arousal pulse was framed and parameterized. Figure 16A is a graph illustrating multiple ultrasonic signals measured in a hole. Figure 16B is a graph illustrating the echoes of the ultrasonic signals of figure 16A estimated by the parameterization process. Figure 16C is a graph illustrating the portions of the measured ultrasonic signals of Figure 16A after removing the extracted echoes from Figure 16B.

Echo Extraction from a Noisy Baseline [00118] To test the effectiveness of the algorithm in extracting the initial echo parameters from the baseline in a snapshot, data from. lab. Echo pulse echoes that had been purchased with an aluminum reflector on a balance ranging from 6 mm to 45 mm were used. Figure 17A is a graph illustrating free field response of ultrasonic transducer. Figure 17B is a graph illustrating the observed pulse echo responses from 6 mm to 45 mm. As shown in figures 17A-17B, there is an inherent touch of the ultrasonic transducer, which obscures the echo that reaches varying levels of severity as balance decreases. To compare the parameter accuracy, the true free field response of the ultrasonic transducer was also recorded, which is shown in figure 17A. For verification, the true free field response can be subtracted from the observed trace that is contaminated with the baseline to obtain the true echo. The value of the arrival time as well as the amplitude of this echo can be compared with this true echo to measure how precisely the obscured echo is extracted. Referring now to Figures 18A-18F, graphs illustrating the decomposition of an ultrasonic signal are shown. The ultrasonic signal is recorded 8. mm away from the reflector. The ultrasonic signal has the tendency removed (for example, using a two-piece linear coupling, coupled and then parameterized.) To illustrate the parameterization result, a waveform recorded using a reflector located 8 mm away from the ultrasonic transducer is used. At this reflector distance the touch baseline significantly contaminates the incoming echo.The objective is to clearly extract the echo from that baseline. [00120] The trace is first preprocessed by removing the exponential, coupled and parameterized trend using a model order of 3 (M = 3) .The removed and controlled trend signal is shown in Figure 18A. Figure 18B is a graph illustrating parametric reconstruction compared to the removed and controlled trend signal in Figure 18A. As shown in Figure 18B, the parameterization approximates the well-removed and well-controlled bias signal, which is also indicated by Figure 18C. In contrast, the difference between the removed and controlled bias signal and the parametric reconstruction. In the region of interest (for example, the location of the main peak and incoming echo rail), the error is around 1%. Figures 18D-18F are graphs illustrating the composition of the reconstruction. Of the three models that make up the reconstruction, the first model (No. 1) is of the highest amplitude. The remaining two echoes (model # 2 and model # 3) are used to represent the baseline (since this portion of the signal is not as well suited to the Gaussian empirical model as the hidden echo in it). Since the first model that makes up the parameterization is assumed to be the true echo, it is desirable to determine how much it compares to the effective echo. For this comparison, the baseline of the signal is removed by subtracting the measured free field response from the transducer. Figures 19A-19C are graphs illustrating the comparison between a true driving echo. a parameterization using a model order of 2 (M = 2) in the traces recorded by an ultrasonic transducer at 10 mm, 20 mm and 30 mm of equilibrium. True echo 1906 is determined by subtracting the free field response from the ultrasonic transducer from the observed echo.1902. The parameterized echo or model 1904 that has the highest amplitude is selected as the echo component. From the coupled signals originally observed, direct deduction of the amplitude and shape of the hidden echo may be difficult, but after parametric extraction the true echo can be clearly revealed. As shown in figures 19A-19C, the parameterized echo 1904 covers well with the true echo response 1906. In all cases, error in the main peaks and echo rails does not exceed 5%, even in near standoffs (10 mm away from reflector). ) where they are significantly obscured by the touch baseline.

Imaging Tests To demonstrate the effectiveness of the parameterization process in terms of imaging parameterization is compared to direct parameter extraction using filtration.

Referring now to Figure 20, a limestone block 2000 (90mm x 76mm x 40mm) used in imaging tests according to implementations - discussed here is shown. For the dataset, the 2000 six-slot limestone block (2.5mm x 28mm) 2002 with variable spacing, for example 2mm, 5mm, 8mm, 10mm, and 12mm as shown, was immersed in water and swept in a 20 mm equilibrium in the horizontal plane parallel to the face of the block. The scan was conducted in 1 mm increments covering 119 mm x 95 mm (eg 11305 samples). The central frequency of the ultrasonic transducer was approximately 375 MHz. [00124] The data set was processed in two modes: first using parameterization and secondly using a filtering method where parameters are directly extracted from the traces observed after the application of a bandpass filter centered near the center frequency of the transducers. In both methods, images were produced using five main echo attributes (eg displacement time, amplitude, bandwidth (or curvature, in case of filtration), center frequency, and phase). Figures 21A-21B are the imaging results for filtration and parameterization, respectively. Because the ultrasonic transducer is operated under ambient pressure, coupling is not optimal resulting in relatively small touch and echo amplitudes. Unlike filtering, parameterization uses the integer signal in the coupling to estimate the echo parameters that results in using more of the signal as a time support in forming the parameter estimate. The merits of this are evident in all five graphs. In general, images produced from echoes characterized by parameterization can solve more detail compared to filtration. Unlike filtering, parameterization uses the entire signal in the window to estimate echo parameters. The merits of this are evident in all five graphs. The color scales of all images were kept equal so that the images were required with a similar dynamic range. When examining the image produced by the echo shift time, it is evident that the block was not exactly parallel to the ultrasonic transducer during the scan. Using parameterization to extract the arrival time, this is clearly visible as the color gradually fades (indicating an increase in travel time due to tilt). The filtered image has a slight color gradation, but the slit detail is not as noticeable. In terms of amplitude, the results look similar, but with parameterization the definition of the leftmost gap is much more visible. By comparing the images generated by bandwidth (or in the case of filtration, curvature), regions with the two closely spaced leftmost slots were resolved in significantly more detail using parameterization. Of all parametric attributes, the center frequency is more sensitive to small changes in swept formation as evidenced by the two most closely spaced slits being resolved. Using filtration, the center frequency image is grainy and has no contrast while using the parametric method, the details in the image are more pronounced (especially in the contrast of the cracks as well as revealing some of the surface texture of the block). Finally, images using incoming echo phasing look similar, but the image produced by parameterization has higher contrast. Although the subject has been described in language specific for structural and / or characteristics. methodological acts, it must be understood that the matter defined in the appended claims does not. is necessarily limited to the specific characteristics or acts described above. Instead, the specific features and acts described above are disclosed as exemplary ways of implementing the claimed subject matter. - CLAIMS -

Claims (20)

1. METHOD FOR AUTOMATICALLY CHARACTERIZING AN ECO IN A ULTRASONIC SIGNAL, the ultrasonic signal being generated with an ultrasonic transducer, the method characterized by the fact that it comprises: a) receiving data corresponding to the ultrasonic signal with the ultrasonic transducer, b) calculating an energy ratio of the ultrasonic signal and locate the echo contained in the ultrasonic signal using the energy ratio; c) - frame a portion of the ultrasonic signal around the localized echo; d) calculating a Fast Fourier Transform (FFT) and a Hilbert envelope of the framed portion of the ultrasonic signal; e) estimating M echo parameter vectors from the Hilbert FFT and envelope of the framed portion of the ultrasonic signal, wherein each of the M vectors c.e echo parameter comprises a plurality of echo parameters; f) calculate M parametric echo models based on each of the M echo parameter vectors; and g) iteratively minimize a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models. Method according to claim 1, characterized in that the calculation of an energy ratio of the ultrasonic signal and the location of the echo contained in the ultrasonic signal using the energy ratio comprises b1. calculate an energy ratio function of the ultrasonic signal, where the energy ratio function is φψ- ±. .Λ. where Ex is energy at a given data point, a and a2 are power adjustment factors, L is a window length, and E is signal energy, f is noise energy. and Et, otal is total energy; and b2. identify a maximum value of the ultrasonic signal energy ratio function, where the maximum value corresponds to an approximate echo location contained in the ultrasonic signal. Method according to claim 2, characterized in that the calculation of an energy ratio function of the ultrasonic signal comprises b3. invert the data corresponding to the head-to-tail ultrasound signal, b4, calculate the inverse ultrasonic signal energy ratio function; and b5. identify a maximum value of the inverted ultrasonic signal energy ratio function, where the maximum value of the ultrasonic signal energy ratio function corresponds to a left rupture of a first echo contained in the ultrasonic signal, and the maximum value of the ultrasonic signal energy function The energy ratio of the inverted ultrasonic signal corresponds to a right rupture of the first echo contained in the ultrasonic signal. Method according to claim 2, characterized in that the calculation of an energy ratio function of the ultrasonic signal comprises: b3, determining the data corresponding to the ultrasonic signal, b4. calculate the energy ratio function of the trimmed ultrasonic signal; and b5. identify a maximum value of the energy ratio function of the trimmed ultrasonic signal, wherein the maximum value of the energy ratio function of the ultrasonic signal corresponds to a left rupture of a first echo contained in the ultrasonic signal, and the maximum value of the The energy ratio of the trimmed ultrasonic signal corresponds to a left rupture of a second echo contained in the ultrasonic signal. Method according to claim 2, characterized in that the window length (L) is approximately equal to -, where s is a tuning coefficient, fc is a central frequency of the ultrasonic signal and fs is a sampling frequency. Method according to claim 1, characterized in that framing a portion of the ultrasonic signal around the localized echo comprises applying a half-Hanning taper to data corresponding to one or more sides of the ultrasonic signal outside the framed portion. of the ultrasonic signal. A method according to claim 1, characterized in that by minimizing a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models, it comprises at least one of a Gauss-Newton optimization ( GN), a genetic algorithm (GA) and a metaheuristic approach to evolutionary optimization, Method according to claim 1, characterized in that the calculation of the M parametric echo models comprises calculating M parametric echo models based on each of the M echo parameter vectors and the framed portion of the ultrasonic signal and wherein iteratively minimizing a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models comprises h. determining the plurality of echo parameters for each of the M echo parameter vectors based on each of the M parametric echo models, i. update the M echo parameter vectors, j. determine if the updated M echo parameter vectors converge with the M echo parameter vectors and k. if convergence is not obtained, calculate M parametric echo models based on each of the updated M echo parameter vectors and the framed portion of the ultrasonic signal and repeat steps (h) - (k). A method according to claim 1, further comprising filtering the data corresponding to the ultrasonic signal to remove at least one baseline component of the ultrasonic signal. Method according to claim 1, characterized in that the plurality of echo parameters comprises at least one of a bandwidth factor (a), an arrival time (τ), a central frequency ( fc), a phase (φ), an amplitude (β) and combinations thereof. 11 Method according to claim 10, characterized in that it further comprises generating an image using the plurality of echo parameters. 12. SYSTEM FOR AUTOMATICALLY CHARACTERIZING AN ECO CONTAINED IN AN ULTRASONIC SIGNAL, characterized by the fact that it comprises: an ultrasonic transducer configured to generate and receive an ultrasonic signal and a unit of. control unit comprising at least one processor and one memory, wherein the control unit is configured for. receive data corresponding to the ultrasonic signal from the ultrasonic transducer, b. calculating an energy ratio of the ultrasonic signal and locating an echo contained in the ultrasonic signal using the energy ratio; ç. frame a portion of the ultrasonic signal around the localized echo; d. calculate a Fast Fourier Transform (FFT) and a Hilbert envelope of the framed portion of the ultrasonic signal, and. estimate M parameters of. echo from the FFT and Hilbert envelope of the framed portion of the ultrasonic signal, wherein each of the M echo parameter vectors comprises a plurality of echo parameters, f. calculate M parametric echo models based on each of the M echo parameter vectors and g. iteratively minimize a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models. System according to claim 12, characterized in that the control unit is configured to calculate an energy ratio of the ultrasonic signal and to locate an echo contained in the ultrasonic signal using the energy ratio of: bl. calculate an energy ratio function of the ultrasonic signal, where the energy ratio function is Ex = α-t (1 /, (i 4. a2 gt), where Ex is energy at a given data point, ax and a2 are power adjusting factors, L · is a window length, is signal energy, Sf = xx_i Et is noise energy and £ cotal is total energy, and b2 identify a maximum value gives the energy ratio function of ultrasonic signal, where the maximum value corresponds to an approximate location of the echo contained in the ultrasonic signal. System according to claim 13, characterized in that the control unit is configured to calculate an energy ratio function of the ultrasonic signal by b3. invert the data corresponding to the head-to-tail ultrasonic signal, b4. calculate the energy ratio function of the inverted ultrasonic signal; and b5. identify a maximum value of the inverted ultrasonic signal energy ratio function, where the maximum value of the ultrasonic signal energy ratio function corresponds to a left rupture of a first echo contained in the ultrasonic signal, and the maximum value of the ultrasonic signal energy function energy ratio of the inverted ultrasonic signal corresponds to a right rupture of the first echo contained in the ultrasonic signal J System according to claim 13, characterized in that the control unit is configured to calculate an energy ratio function of the ultrasonic signal by b3. ascertain the data corresponding to the ultrasonic signal, b4. calculate the energy ratio function of the trimmed ultrasonic signal; and b5. identify a maximum value of the energy ratio function of the trimmed ultrasonic signal, wherein the maximum value of the energy ratio function of the ultrasonic signal corresponds to a left rupture of a first echo contained in the ultrasonic signal, and the maximum value of the The energy ratio of the trimmed ultrasonic signal corresponds to a left rupture of a second echo contained in the ultrasonic signal. The system of claim 12, wherein the control unit is configured to frame a portion of the ultrasonic signal around the localized echo comprising applying a half-Hanning taper to data corresponding to one or more. sides of the ultrasonic signal outside the framed portion of the ultrasonic signal around the localized echo. System according to claim 12, characterized in that the control unit is configured to iteratively minimize a difference between the framed portion of the ultrasonic signal and one. sum of the M parametric echo models by performing at least one of a Gauss-Newton optimization (GN), a genetic algorithm (GA) and a metaheuristic approach to evolutionary optimization. System according to claim 12, characterized in that the control unit is configured to calculate M parametric echo models by calculating M parametric echo models based on each of the M echo parameter vectors and the framed portion of the ultrasonic signal and wherein the control unit is configured to iteratively minimize a difference between the framed portion of the ultrasonic signal and a sum of the M parametric echo models per h. determining the plurality of echo parameters for each of the M echo parameter vectors based on each of the M parametric echo models, i. update the M echo parameter vectors, j. determine if the updated M echo parameter vectors converge with the M echo parameter vectors and k. if convergence is not obtained, calculate M parametric echo models based on each of the updated M echo parameter vectors and the framed portion of the ultrasonic signal and repeat steps (h) ~ (k), System according to claim 12, characterized in that the plurality of echo parameters comprises at least one of a bandwidth factor (a), an arrival time (τ), a central frequency (fc ), a phase (<p), an amplitude (3) and combinations thereof. System according to claim 19, characterized in that the control unit is further configured to generate an image using the plurality of echo parameters.